This paper starts with an informal introduction to inquisitive semantics. After that, we present a formal definition of the semantics, and introduce the basic semantic notions of inquisitiveness and informativeness, in terms of wich we define the semantic categories of questions, assertions, and hybrid sentences.The focus of this paper will be on the logical pragmatical notions that the semantics gives rise to. We introduce and motivate inquisitive versions of principles of cooperation, which direct a conversation towards enhancement of the common ground. We define a notion of compliance, which judges relatedness of one utterance to another, and a notion of homogeneity, which enables quantitative comparison of compliant moves. We end the paper with an illustration of the cooperative way in which implicatures are established, or cancelled, in inquisitive pragmatics.